Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexStarted [[weak equivalence of internal categories]]. Needs some more work, including examples and theorems.

   Started weak equivalence of internal categories. Needs some more work, including examples and theorems.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIn a topos one takes epis, not regular epis for $J$ ?

   In a topos one takes epis, not regular epis for $J$ ?

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAll epis are regular in a topos. In a regular category you take regular epis. Although there is nothing that says $J$ has to be subcanonical (for example, take the pretopology on $Top$ of locally split maps).

   All epis are regular in a topos. In a regular category you take regular epis. Although there is nothing that says $J$ has to be subcanonical (for example, take the pretopology on $Top$ of locally split maps).

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2012
   • (edited May 17th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn a topos every epimorphism is regular (and effective)! [edit: I see I overlapped with David.]

   In a topos every epimorphism is regular (and effective)!

   [edit: I see I overlapped with David.]

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added pointers to the entry from _[[internal category]]_ and _[[equivalence of categories]]_. I have also added under _Related concepts_ a pointer to _[[anafunctor]]_, which I guess you may want to come back to. Notice that at _[[internal category]]_ there is a paragraph on "ana-equivalences".

   I have added pointers to the entry from internal category and equivalence of categories. I have also added under Related concepts a pointer to anafunctor, which I guess you may want to come back to. Notice that at internal category there is a paragraph on “ana-equivalences”.

6. • CommentRowNumber6.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexThanks, Urs.

   Thanks, Urs.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexOh, and I have added the Context-table of contents _[[internal infinity-categories contents|internal categories]]_.

   Oh, and I have added the Context-table of contents internal categories.

8. • CommentRowNumber8.
   • CommentAuthorTim_Porter
   • CommentTimeAug 29th 2021
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexActivated some author links <a href="https://ncatlab.org/nlab/revision/diff/weak+equivalence+of+internal+categories/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/weak+equivalence+of+internal+categories/7">v7</a>, <a href="https://ncatlab.org/nlab/show/weak+equivalence+of+internal+categories">current</a>

   Activated some author links

   diff, v7, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeAug 29th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexHave adjusted the wording and hyperlinking of the Idea-section, for clarity and flow. <a href="https://ncatlab.org/nlab/revision/diff/weak+equivalence+of+internal+categories/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/weak+equivalence+of+internal+categories/8">v8</a>, <a href="https://ncatlab.org/nlab/show/weak+equivalence+of+internal+categories">current</a>

   Have adjusted the wording and hyperlinking of the Idea-section, for clarity and flow.

   diff, v8, current